ALPS-users,
I am investigating the excitations of a Heisenberg exchange coupled S=1 spin cluster as a function
of applied magnetic field and temperature. All exchange constants are antiferromagnetic, and
the system can be thought of as a collection of a weakly coupled dimers. I am starting with just
6 spins and will increase the elements later. There are two exchanges and a single ion anisotropy
term (D) included in the Hamiltonian. The GRAPH and HAMILTONIAN are pasted at the end
of this message.
For a given temperature and magnetic field, I would like to calculate the energy, S total quantum
number , and Sz total quantum number of the ground state and its excitations.
The total spin quantum number S, corresponds to the sum of the spin
vectors squared:
S^2 = (S_1 + S_2 + S_3 + ...)^2, and
the Sz total quantum number corresponds to the sum of the S_nz values.
Sz = S_1z + S_2z + S_3z + ...
Which algorithm do you suggest using for this problem? Eventually, I would like to extend the
lattice to 12 spins and larger if possible. Ultimately, I would like to know the ~10
lowest energy states and their S and Sz quantum numbers as a function of applied magnetic
field.
I am a beginner at ALPS, and have worked through some of the tutorials. Any
suggestions would be very much appreciated.
Thanks,
Matthew Stone
----- dimerplanegraph.xml file-----
<LATTICES>
<!--
3 vertical dimers forming a triangle
-->
<GRAPH name="3dimers1plane" vertices="6">
<VERTEX id="1"></VERTEX>
<VERTEX id="2"></VERTEX>
<VERTEX id="3"></VERTEX>
<VERTEX id="4"></VERTEX>
<VERTEX id="5"></VERTEX>
<VERTEX id="6"></VERTEX>
<EDGE type="0" source="1" target="2"/>
<EDGE type="0" source="3" target="4"/>
<EDGE type="0" source="5" target="6"/>
<EDGE type="1" source="2" target="4"/>
<EDGE type="1" source="2" target="6"/>
<EDGE type="1" source="4" target="6"/>
<EDGE type="1" source="1" target="3"/>
<EDGE type="1" source="1" target="5"/>
<EDGE type="1" source="3" target="5"/>
</GRAPH>
</LATTICES>
-----------------------------------------------
-----model-dspin.xml file-----
<MODELS>
<HAMILTONIAN name="BaMnO">
<PARAMETER name="J0" default="J"/>
<PARAMETER name="J1" default="J"/>
<PARAMETER name="J" default="1"/>
<PARAMETER name="h" default="0"/>
<PARAMETER name="D" default="0"/>
<BASIS ref="mixed spin"/>
<SITETERM site="i">
-h*Sz(i) + D*Sz(i)*Sz(i)
</SITETERM>
<BONDTERM type="0" source="i" target="j">
J0*Sz(i)*Sz(j)+J0/2*(Splus(i)*Sminus(j)+Sminus(i)*Splus(j))
</BONDTERM>
<BONDTERM type="1" source="i" target="j">
J1*Sz(i)*Sz(j)+J1/2*(Splus(i)*Sminus(j)+Sminus(i)*Splus(j))
</BONDTERM>
</HAMILTONIAN>
<BASIS name="mixed spin">
<SITEBASIS type="0" ref="spin">
<PARAMETER name="local_spin" value="local_S"/>
<PARAMETER name="local_S" value="1"/>
</SITEBASIS>
<SITEBASIS type="1" ref="spin">
<PARAMETER name="local_spin" value="local_S'"/>
<PARAMETER name="local_S'" value="1"/>
</SITEBASIS>
<CONSTRAINT quantumnumber="Sz" value="Sz_total"/>
</BASIS>
<SITEBASIS name="spin">
<PARAMETER name="local_spin" default="local_S" />
<PARAMETER name="local_S" default="1/2" />
<QUANTUMNUMBER name="S" min="local_spin" max="local_spin" />
<QUANTUMNUMBER name="Sz" min="-S" max="S" />
<OPERATOR name="Splus" matrixelement="sqrt(S*(S+1)-Sz*(Sz+1))">
<CHANGE quantumnumber="Sz" change="1" />
</OPERATOR>
<OPERATOR name="Sminus" matrixelement="sqrt(S*(S+1)-Sz*(Sz-1))">
<CHANGE quantumnumber="Sz" change="-1" />
</OPERATOR>
<OPERATOR name="Sz" matrixelement="Sz" />
</SITEBASIS>
</MODELS>
--------------------------------------------------
Thank you,
Matthew B. Stone
Neutron Scattering Science Division
Oak Ridge National Laboratory
PO box 2008 MS6475
Oak Ridge, TN 37831-6475
Phone: 1-865-202-6898
Fax: 1-865-574-6080